1.3.1: Preparation N.3

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Simple Interest can be defined as interest paid or computed on only the original principal of a loan or on the amount of an account. You may have seen the formula for Simple Interest before:

\[ I = Prt \nonumber\]

where I is the interest, P is the principal (or amount) of the loan, r is the annual interest rate in decimal form, and t is the number of years.

(1) If the interest rate on a loan is doubled, what will be the effect on the total amount of interest paid on the loan? Assume simple interest is used. Choose all that apply.

(i) The total amount of interest paid on the loan will be twice as much.

(ii) The total amount of interest paid on the loan will remain the same.

(iii) The total amount of interest paid on the loan will go up by the same percentage as the percentage point increase in the interest rate.

(iv) The total amount of interest paid on the loan will be four times as much as the original amount.

(v) The total amount of interest paid on the loan will double.

PayPal is a company that operates an online payments system that is used by many vendors to receive payments from customers. Once users link their credit cards or bank accounts to PayPal, they can pay for things online without having to re-enter their sensitive card or bank details.

PayPal has a service called “PayPal Credit.” Some vendors provide a special offer of “No Payments + No Interest” if the original charges are paid in full within six months (sometimes the offer is only available for a minimum purchase of $250).

Marco is looking to purchase a new laptop computer which costs $1,200. He is considering a payment plan that would give him six months to pay for the computer, with no interest charged. For the purposes of Questions 2–4, we will assume there are no taxes or other fees that would increase the total cost of the laptop.

(2) The federal government sets a minimum wage that is currently $7.25 an hour. Most states have a minimum wage that is equal to or higher than $7.25 an hour. Wisconsin is a state with a minimum wage that is the same as the federal minimum wage. If Marco is working at a minimum wage job full time (40 hours per week) in Wisconsin, how much is his weekly salary?

(3) Using the weekly salary you calculated above, how much would Marco earn per month (assume that there are four weeks in every month)?

(4) What percentage of his monthly salary should Marco set aside to pay for the laptop within six months? As mentioned, the new laptop computer costs $1,200. Marco is considering a payment plan that would give him six months to pay for the computer, with no interest charged. Assume there are no taxes or other fees that would increase the total cost of the laptop. Round to the nearest hundredth of a percent (two decimal places). Hint: Use Marco’s income as calculated in Question 3.

(5) In 2023, the minimum wage in Michigan was raised to $10.10 an hour. For parts (a)-(c), assume a working week of 40 hours.

(a) How much is his weekly salary?

(b) How much would he earn per month? Assume there are four weeks in every month.

(c) What percentage of his monthly salary should Marco set aside to pay for the laptop within six months? Recall that the laptop costs $1200. Round to two decimal places.

(6) When you make payments on a long-term loan with interest, a portion of each monthly payment goes to pay the current interest due on the loan, and the remaining amount of the monthly payment is used to pay down the amount still owed on the loan (i.e., the remaining principal). Ding-Huan is purchasing a car and is paying an Annual Percentage Rate (APR) of 6%. After making a down payment, the amount Ding-Huan financed was $15,000 and his monthly payment for the 5-year term (length) of the loan is $290.00. You can think of the calculations for the portion going to interest and principal each month as simple interest problems, calculated month by month. Recall that I = Prt for simple interest.

(a) Calculate the total amount that Ding-Huan will pay over the 5-year term. How much will be principal? How much will be interest?

Total =

Principal =

Interest =

(b) How much will the monthly interest rate be, given as a percent?

(c) How much of the first monthly payment goes toward paying off the interest and how much goes toward paying off the principal? Round to the nearest cent.

(d) How much will Ding-Huan still owe on the principal after he makes the first payment (at the end of the first month of the loan)? Recall that he borrowed $15,000.

(e) How much will he still owe on the principal after he makes the second payment at the end of the second month of the loan? Round to the nearest cent.

(7) In the next collaboration, we will be discussing college student loan debt. If about 44 million Americans had student loan debt in 2021, with an average debt of around $37,000, estimate how much total student loan debt was outstanding at that time.

After Preparation N.3 (survey)

You should be able to do the following things for the next collaboration. Rate how confident you are on a scale of 1–5 (1 = not confident and 5 = very confident).

Before beginning Collaboration N.3, you should understand the concepts and demonstrate the skills listed below:

Skill or Concept: I can …	Rating from 1 to 5
convert percentages to decimals.
decide when simple interest is appropriate and how to calculate it.
use and interpret the terms “millions,” “billions,” and “trillions.”

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